M.Sc. Management at TUM

Exam

09.02.2026, 08:00 – 10:00
120min, Multiple Choice

Grade Distribution WS25

Resources

• Moodle
• Syllabus
• Formula Sheet
• Exercise Exam 01 (Solutions), Exercise Exam 02 (Solutions)
• Possibly Outdated Exercise Exam

Lecture

Mondays 15:00 – 16:30, 20.10. – 02.02.
Thursdays 11:30 – 13:00, 16.10. – 05.12.
Christian Feilcke
macher*

Topics

Microecononomics

• Specialization & Trade
• Consumption and Demand
• Production and Supply
• Perfect Competition
• Market Failure

Macroeconomics

• Macroeconomic Indicators
• Economic Growth
• Economic Fluctuations

What is Economics?

• Studies how individuals and societies allocate scarce resources to satisfy their wants. Fundamentally a choice problem under scarcity, involving the weighing of benefits and costs. (p. 3)
• Classic definitions:
  • “A calculus of pleasure and pain” (Jevons, 1871)
  • “A study of mankind in the ordinary business of life” (Marshall, 1890)
  • “The science which studies human behaviour as a relationship between ends and scarce means which have alternative uses” (Robbins, 1932)
• Microeconomics: Analyzes the behavior of individuals and firms and their interaction on markets. (p. 4)
  • Consumption and Demand
  • Production and Supply
  • Perfect Competition
  • Market Failure
• Macroeconomics: Analyzes the behavior of the economy as a whole.
  • Macroeconomic Indicators
  • Economic Growth
  • Economic Fluctuations

Stuff I was a little stuck on

• Surpluses
• Welfare Loss
• Cost function
• Thresholds
• Substitution/Income Effects

Preparation Calculations

MRS/MRTS for common functions

Cobb-Douglas ($q_1^{\alpha }\cdot q_2^{\beta }$ or $L^{\alpha }\cdot K^{\beta }$):

$MRS=\frac{\alpha }{\beta }\cdot \frac{q_2}{q_1}MRTS=\frac{\alpha }{\beta }\cdot d\frac{K}{L}$

(obviously, the first term cancels for functions like $(LK{)}^{\alpha }$)

Simplified CES ($q_1^{\alpha }+q_2^{\alpha }$ or $L^{\alpha }+K^{\alpha }$):

$MRS={\left(\frac{q_1}{q_2}\right)}^{\alpha -1}{\left(\frac{L}{K}\right)}^{\alpha -1}$

Quasilinear ($f(q_1)+a{q}_2$):

$MRS=\frac{f^{\prime }(q_1)}{a}$

Chapter 1: Specialization & Trade

None, really. Maybe set up the comparative advantage table.

Chapter 2: Consumption and Demand (2)

• Marginal Rate of Substitution (MRS): $M{U}_{q1}/M{U}_{q2}$
  • Shortcuts see above
  • Otherwise get from marginal utilities
• Optimal Consumption: $MRS=\frac{p_1}{p_2}$, solve for one good, sub into budget constraint for the other
  • Cobb-Douglas ($q_1^{\alpha }\cdot q_2^{\beta }$): $q_1^{\ast }=\frac{\alpha }{\alpha +\beta }\cdot \frac{y}{p_1},q_2^{\ast }=\frac{\beta }{\alpha +\beta }\cdot \frac{y}{p_2}$
  • Simplified CES ($q_1^{\alpha }+q_2^{\alpha }$): Let substitution elasticity $\sigma =\frac{1}{1-\alpha }$. Then $q_1^{\ast }=\frac{y\cdot p_1^{-\sigma }}{p_1^{1-\sigma }+p_2^{1-\sigma }},q_2^{\ast }=\frac{y\cdot p_2^{-\sigma }}{p_1^{1-\sigma }+p_2^{1-\sigma }}$
  • Quasilinear ($f(q_1)+a{q}_2$): First determine $q_1$ using $\frac{f^{\prime }(q_1)}{a}=\frac{p_1}{p_2}$, then $q_2^{\ast }=\frac{y-p_1{q}_1^{\ast }}{p_2}$

Probably Useful

• Normal/Inferior, Regular/Giffen: Normal/Inferior is $y\sim p$, Regular/Giffen is $q\sim p$
  • Cobb-Douglas: Both goods are always normal and regular.
  • Quasilinear: Good 1 is normal if $f$ is concave ($f^{\prime \prime }<0$), inferior if convex; Good 2 is always normal. Both regular.

Chapter 3: Production and Supply (2)

• Marginal Rate of Technical Substitution (MRTS): $M{P}_L/M{P}_K$
  • Shortcuts see above
  • Otherwise get from marginal products
• Optimal Production: Set $MRTS=\frac{w}{r}$, solve for one input, sub into $F(L,K)$ for the other, then backsub into first
  • For Simplified Cobb-Douglas ($(L\cdot K{)}^{\alpha }$): $L^{\ast }={\left(\frac{r}{w}\right)}^{\frac{1}{2}}\cdot q^{\frac{1}{2\alpha }},K^{\ast }={\left(\frac{w}{r}\right)}^{\frac{1}{2}}\cdot q^{\frac{1}{2\alpha }}$
  • For Simplified CES ($L^{\alpha }+K^{\alpha }$): $L^{\ast }={\left(\frac{w}{r}\right)}^{\frac{1}{\alpha -1}}{\left(\frac{q}{1+{\left(\frac{w}{r}\right)}^{\frac{\alpha }{\alpha -1}}}\right)}^{\frac{1}{\alpha }}$

Probably Useful

• Returns to Scale: Depends on extracted factor $\lambda$: Decr. < 1 < Increasing
  • Simplified CES: $\lambda =\alpha$
  • Cobb-Douglas: $\lambda =\alpha +\beta$
• Thresholds:
  • Short-Run: $MC=AVC$ to get $AV{C}_{min}$ or $p_{shutdown}$
  • Long-Run: $MC=AC$ to get $A{C}_{min}$ or $p_{min}$
  • Threshold shortcut: If the cost function is of the form $C(q)=a{q}^2+bq+c^f$, then $p_{min}=2\sqrt{a{c}^f}+b$

Chapter 4: Perfect Competition (5)

• Marginal Cost: Derivative of $C(q)$
• Average Cost, Average Variable Cost: $C(q)/q$
• Individual Supply: Set $MC=p$, solve for $q(p)$
• Break-Even Quantity: Set $MC=AC$, solve for $q^{\ast }$ (this implies $\pi =0$ and therefore the long-run exit)
• Equilibrium Price (long-run): $p^{\ast }=MC(q^{\ast })$

Chapter 5: Market Failure

Monopolies

• Marginal Cost: Derivative of $C(Q)$
• Price Function: Set $p=Q^D(p)$, solve for $p(Q)$
• Revenue and Marginal Revenue: $p(Q)\cdot Q$ and its derivative
• Equilibrium Quantity: Set $MR=MC$, solve for $Q^{\ast }$
• Equilibrium Price: $p^{\ast }=p(Q^{\ast })$

Probably Useful

• Socially Optimal: $p(Q)=MC$
• Fair Return: $p(Q)=AC$

Externalities

• Marginal Cost: Derivative of $C_i(Q)$
• Social Marginal Cost: $SMC=MC+M{C}_{Ex}$
• Price Function: Set $p=Q^D(p)$, solve for $p(Q)$
• Optimal Quantity: For individual, $p=MC$, for welfare $p=SMC$, solve for $q_i^{\ast }$, assume $Q^{\ast }=n{q}_i^{\ast }$.

Public Goods

• Marginal Cost: Derivative of $C(Q)$
• Sum of Marginal Benefits: $\sum M{B}_i(Q)$
• Optimal Quantity For individual, $MB=MC$, for efficient/welfare, $\sum MB=MC$

Chapter 6: Macroeconomic Indicators

None, really.

Chapter 7: Economic Growth (1/4)

• Output per Worker: $f=\frac{F(L,K)}{L}$ with $k=\frac{K}{L}$
  • Cobb-Douglas Shortcut ($L^{\alpha }{K}^{1-\alpha })$: $k^{1-\alpha }$

Shortcuts for Cobb-Douglas ($L^{\alpha }{K}^{1-\alpha })$

• Golden Rule Saving Rate for CD: $s_{gold}^{\ast }=1-a$
• Capital per Worker for CD: $k^{\ast }=(\frac{s}{\delta +n}{)}^{\frac{1}{\alpha }}$
• Consumption per Worker for CD: $c^{\ast }=\alpha (\frac{s}{\delta +n}{)}^{\frac{1-\alpha }{\alpha }}$

Chapter 8: Economic Fluctuations (3)

• IS Curve: $Y=C(Y-T)+I(r)+G$, solve for $Y$
• LM Curve: $\frac{M}{P}=L(Y,r)$, solve for $r$
• IS-LM Equilibrium: Set $Y$ from IS equal to $Y$ from LM, then solve for whatever you need

Probably Useful

• Goods Market Marginal Government Spending Multiplier: $\frac{1}{1-MPC}$ where $MPC=\frac{dC}{d(Y-T)}$
• Tax Multiplier is the negative of the government multiplier times $MPC$: $-\frac{MPC}{1-MPC}$
• For general impacts of changes in $G$/$M$/$T$, [see the table](obsidian://adv-uri?vault=TUM&filepath=Principles%20of%20Economics%2FEconomic%20Fluctuations.md&block=nb1aa1](obsidian://adv-uri?vault=TUM&filepath=Principles%20of%20Economics%2FEconomic%20Fluctuations.md&block=d2k8t1) (section link for web version)